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May 1997 Functional large deviation principles for first-passage-time processes
Anatolii A. Puhalskii, Ward Whitt
Ann. Appl. Probab. 7(2): 362-381 (May 1997). DOI: 10.1214/aoap/1034625336

Abstract

We apply an extended contraction principle and superexponential convergence in probability to show that a functional large deviation principle for a sequence of stochastic processes implies a corresponding functional large deviation principle for an associated sequence of first-passage-time or inverse processes. Large deviation principles are established for both inverse processes and centered inverse processes, based on corresponding results for the original process. We apply these results to obtain functional large deviation principles for renewal processes and superpositions of independent renewal processes.

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Anatolii A. Puhalskii. Ward Whitt. "Functional large deviation principles for first-passage-time processes." Ann. Appl. Probab. 7 (2) 362 - 381, May 1997. https://doi.org/10.1214/aoap/1034625336

Information

Published: May 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0885.60023
MathSciNet: MR1442318
Digital Object Identifier: 10.1214/aoap/1034625336

Subjects:
Primary: 60F10
Secondary: 60G55 , 60K05

Keywords: contraction principle , counting processes , first passage times , inverse processes , large deviation principle , large deviations , renewal processes , Skorohod topologies , superpositions of renewal processes

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 2 • May 1997
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